Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Moshe Stupel, Shula Weissman and Avi(Berman) Sigler
Pages: [67] - [92]
Received Date: February 18, 2019; Revised April 14, 2019
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122033
The methods of teaching and instruction in mathematics are derived
from the program of studies and its goals. One of the principal goals
of studies of mathematics is to provide the students with methods of
reasoning that may assist them in other fields of study and knowledge,
and to develop such methods.
The meaning of “learning to think” is: the teacher of mathematics
should develop the ability of students to apply information, perform
analysis and synthesis at an adequate level, of basic properties,
rules and the theorems that they studied at an earlier stage of the
teaching process.
By using methods of solution and knowledge from other fields of
mathematics one can obtain simpler and faster solutions.
Finding another method of solution by using the same mathematical
field, and especially from another field, contributes to development
of reasoning and raises it to a higher level.
Implementation of previous knowledge in a new situation that results
in a shorter and simpler solution or a more beautiful solution
increases enjoyment and satisfaction from studies of the subject.
Integration of fields in problem solution gives the students and wider
outlook to mathematics as a comprehensive discipline, while creating
connections between its different branches.
The ability to handle different tasks in Euclidean geometry, some of
which are hard or complex, depends to a large extent on the
“mathematical toolbox” available to student. The wider and richer
it is with lesser-known theorems and formulas, the much higher is the
student’s ability to cope such problems, and it is very likely that
they will be able to achieve elegant, short and aesthetic solutions.
In order to illustrate the importance of the “mathematical
toolbox”, we present seven interesting tasks in Euclidean geometry
that require theorems and formulas which are not usually known to the
students. In six of the tasks we presented more than one solution.
Usually the solution obtained by an unknown theorem or formula is
surprising, short and the prettiest of all the solutions.
lesser-known theorems, elegant solutions, mathematical toolbox.
